limits

**johntuan** · October 4th 2008, 07:36 PM

Find the Limit.

lim x->oo sqrt(x^2+1)

oo=infinity

**ThePerfectHacker** · October 4th 2008, 07:37 PM

Originally Posted by johntuan

Find the Limit.

lim x->oo sqrt(x^2+1)

oo=infinity

$\sqrt{x^2+1} \geq \sqrt{x^2+0} = \sqrt{x^2} = x$ for $x>0$ .

And $\lim_{x\to \infty} x = \infty$ so $\lim_{x\to \infty}\sqrt{x^2+1} = \infty$ .

**johntuan** · October 4th 2008, 07:43 PM

how come the 1 turns to a 0?

**ThePerfectHacker** · October 4th 2008, 07:44 PM

Originally Posted by johntuan

how come the 1 turns to a 0?

It does not. It use " $\geq$ " there.

Basically I am showing that $\sqrt{x^2+1}$ is larger than $x$ . And since $x$ goes to $\infty$ must mean $\sqrt{x^2+1}$ goes to $\infty$ .

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